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0606/11 Oct/Nov 2025, Question 3: Solving Exponential and Log Equations

Cambridge IGCSE Additional Mathematics 0606 · Paper 11 (Non-calculator) · Non-calculator · 9 marks

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The question, in short

Solve two equations: a logarithmic equation in base 2 and x, and an exponential equation involving e with x² terms.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 5 marks

Solve log₂ x − 4 = 5 log_x 2 for x.

  1. 1Change of base: log_x 2 = 1/log₂ x
  2. 2log₂ x − 4 = 5/log₂ x ⇒ (log₂ x)² − 4 log₂ x − 5 = 0
  3. 3(log₂ x − 5)(log₂ x + 1) = 0
  4. 4log₂ x = 5 or −1
  5. 5x = 2⁵ = 32 or x = 2⁻¹ = 1/2

Answerx = 32 or x = 1/2

Part (b) · 4 marks

Solve e^(x² − 3) = 25e^(7 − x²) for x.

  1. 1Divide: e^(x² − 3 − (7 − x²)) = 25
  2. 2e^(2x² − 10) = 25
  3. 32x² − 10 = ln 25
  4. 4x² = (ln 25 + 10)/2 = 5 + ln 5
  5. 5x = ±√(5 + ln 5)

Answerx = ±√(5 + ln 5)

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Also searched as: 0606/11/O/N/25 · 0606_w25_qp_11 · 0606 w25 11 · question 3.
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